最小化机械臂运动时间“3-5-3”轨迹优化粒子群算法matlab完整代码

以下是一个简单的“3-5-3”轨迹优化粒子群算法的Matlab代码，目标函数是最小化机械臂运动时间：

% 机械臂“3-5-3”轨迹优化粒子群算法

% 定义问题
goal = 'min_time'; % 最小化机械臂运动时间
num_joints = 6; % 机械臂关节数量
num_particles = 40; % 粒子数量
num_iterations = 100; % 迭代次数

% 定义变量
lb = [-pi/2, -pi/2, -pi/2, -pi/2, -pi/2, -pi/2]; % 下限
ub = [pi/2, pi/2, pi/2, pi/2, pi/2, pi/2]; % 上限
num_vars = 2*num_joints; % 变量数

% 粒子群初始化
particles = repmat(struct('position', [], 'velocity', [], 'fitness', [], 'best_position', [], 'best_fitness', []), num_particles, 1);
for i = 1:num_particles
    particles(i).position = lb + (ub - lb).*rand(1, num_vars);
    particles(i).velocity = zeros(1, num_vars);
    particles(i).fitness = feval(@objective, particles(i).position, goal);
    particles(i).best_position = particles(i).position;
    particles(i).best_fitness = particles(i).fitness;
end

% 迭代优化
global_best_fitness = inf; % 全局最优适应度
global_best_position = zeros(1, num_vars); % 全局最优位置
for i = 1:num_iterations
    for j = 1:num_particles
        % 更新速度和位置
        particles(j).velocity = particles(j).velocity + rand(1, num_vars).*(particles(j).best_position - particles(j).position) + rand(1, num_vars).*(global_best_position - particles(j).position);
        particles(j).position = particles(j).position + particles(j).velocity;
        % 检查约束条件
        particles(j).position = max(particles(j).position, lb);
        particles(j).position = min(particles(j).position, ub);
        % 评估适应度
        particles(j).fitness = feval(@objective, particles(j).position, goal);
        % 更新个体最优位置和全局最优位置
        if particles(j).fitness < particles(j).best_fitness
            particles(j).best_position = particles(j).position;
            particles(j).best_fitness = particles(j).fitness;
        end
        if particles(j).best_fitness < global_best_fitness
            global_best_fitness = particles(j).best_fitness;
            global_best_position = particles(j).best_position;
        end
    end
    % 输出当前最优适应度
    disp(['Iteration ', num2str(i), ': Best Fitness = ', num2str(global_best_fitness)]);
end

% 优化结果
disp('Optimization Results:');
disp(['Best Fitness = ', num2str(global_best_fitness)]);
disp(['Best Position = ', num2str(global_best_position)]);

% 目标函数
function fitness = objective(position, goal)
    % 解码变量
    num_joints = length(position)/2;
    q_dot_max = [pi/2, pi/2, pi/2, pi/2, pi/2, pi/2]; % 最大关节角速度
    a_max = [2, 2, 2, 2, 2, 2]; % 最大加速度
    q = zeros(1, num_joints);
    q_dot = zeros(1, num_joints);
    a = zeros(1, num_joints);
    for i = 1:num_joints
        q(i) = position(i);
        q_dot(i) = position(i+num_joints);
        a(i) = (q_dot(i)^2)/2;
    end
    % 计算时间
    if strcmp(goal, 'min_time')
        fitness = 0;
        for i = 1:num_joints
            % 加速
            t_acc = abs(q_dot(i))/a_max(i);
            q_acc = sign(q_dot(i))*0.5*a_max(i)*t_acc^2;
            if abs(q_acc) > abs(q(i))
                t_acc = sqrt(2*abs(q(i))/a_max(i));
                q_acc = sign(q(i))*0.5*a_max(i)*t_acc^2;
                q_dot(i) = sign(q_acc)*sqrt(2*abs(q(i))*a_max(i));
                a(i) = a_max(i);
            end
            % 匀速
            t_const = (abs(q(i)) - 2*abs(q_acc))/abs(q_dot(i));
            % 总时间
            t_total = 2*t_acc + t_const;
            fitness = fitness + t_total;
        end
    end
end

需要注意的是，此代码仅提供了一个基本的实现思路，具体实现需要根据具体问题进行调整。另外，需要自己编写约束函数，以确保优化结果符合机械臂的运动规律和限制条件。